\(A=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}.\frac{36}{35}......\frac{9801}{9800}=\frac{\left(2.3.4.5....99\right)^2}{1.3.2.4.3.5.4.6.....98.100}=\frac{2.3.4.5...99}{1.2.3.4.....98}.\frac{2.3.4.5....99}{3.4.5.6......100}=\frac{99}{1}.\frac{2}{100}=\frac{99}{50}\)

A=4/3.9/8.16/15.25/24. ... .9801/9800

Tính được chưa

#)Giải :

\(1\frac{1}{3}\times1\frac{1}{8}\times1\frac{1}{15}\times...\times1\frac{1}{9800}\)

\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times...\times\frac{9801}{9800}\)

\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times\frac{4.4}{3.5}\times...\times\frac{99.99}{98.100}\)

\(=\frac{2.3.4.....99}{1.2.3.....98}\times\frac{2.3.4.....99}{3.4.5.....100}\)

\(=99\times\frac{2}{100}=\frac{198}{100}=\frac{99}{50}\)

\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times...\times\frac{9801}{9800}\)

\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times\frac{4.4}{3.5}\times...\times\frac{99.99}{98.100}\)

\(=\frac{2.3.4.5.....99}{1.2.3.4....98}\times\frac{2.3.4.5.....99}{3.4.5.6.....100}\)

\(=\frac{99}{1}\times\frac{2}{100}\)

\(=\frac{99}{50}\)

\(1\frac{1}{3}\times1\frac{1}{8}\times1\frac{1}{15}\times........\times1\frac{1}{9800}\)

\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times.......\times\frac{9801}{9800}\)

\(=\frac{2\times2}{1\times3}\times\frac{3\times3}{2\times4}\times\frac{4\times4}{3\times5}\times......\times\frac{99\times99}{98\times100}\)

\(=2\times\left(\frac{2}{3}\times\frac{3}{2}\times\frac{3}{4}\times\frac{4}{3}\times.....\times\frac{99}{98}\times\frac{99}{100}\right)\)

\(=2\times\frac{99}{100}\)

\(=\frac{198}{100}=\frac{99}{50}\)

\(1\frac{1}{30}:\left(24\frac{1}{6}-24\frac{1}{5}\right)-\frac{1\frac{1}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(-1\frac{1}{15}\right):\left(8\frac{1}{5}-8\frac{1}{3}\right)\)

\(\Rightarrow\frac{31}{30}:\left(\frac{145}{6}-\frac{121}{5}\right)-\frac{\frac{3}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{41}{5}-\frac{25}{3}\right)\)

\(\Rightarrow\frac{31}{30}:\left(\frac{725}{30}-\frac{726}{30}\right)-\frac{\frac{6}{4}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{123}{15}-\frac{125}{15}\right)\)

\(\Rightarrow\frac{31}{30}:\frac{-1}{30}-\frac{\frac{3}{4}}{4x-\frac{1}{2}}=\frac{-16}{15}:\frac{-2}{15}\)

\(\Rightarrow\frac{31}{30}.\frac{30}{-1}-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\frac{-16}{15}.\frac{15}{-2}\)

\(\Rightarrow\left(-31\right)-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=8\)

\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-31\right)-8\)

\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-39\right)\)

\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}:\left(-39\right)\)

\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}.\frac{-1}{39}\)

\(\Rightarrow4x-\frac{1}{2}=\frac{-1}{52}\)

\(\Rightarrow4x=\frac{-1}{52}+\frac{1}{2}\)

\(\Rightarrow4x=\frac{-1}{52}+\frac{26}{52}\)

\(\Rightarrow4x=\frac{25}{52}\)

\(\Rightarrow x=\frac{25}{52}:4\)

\(\Rightarrow x=\frac{25}{52}.\frac{1}{4}\)

\(\Rightarrow x=\frac{25}{208}\)

Vậy \(x=\frac{25}{208}\)

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